In late October, 1988, a survey was conducted by CBS News of 1500 adults in the United States to find out their preferences in the upcoming presidential election. Out of 1500 persons, y1 = 750 supported George Bush, y2 = 650 supported Michael Dukakis, and y3 = 100 supported other candidates or expressed no opinion. Assume that the data y = (y1,y2,y3) follow the multinomial distribution with parameters (01, 02, 03). a. Find a conjugate prior for (01, 02, 03). b. Define a noninformative prior for (01, 02, 03). c. Assume that p(01, 02, 03) ∞ 010203. Find the posterior distribution of (01, 02, 03) given data y.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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In late October, 1988, a survey was
conducted by CBS News of 1500 adults in
the United States to find out their
preferences in the upcoming presidential
election. Out of 1500 persons, y1 = 750
supported George Bush, y2 = 650
supported Michael Dukakis, and y3 = 100
supported other candidates or expressed
no opinion. Assume that the data y =
(y1,y2,y3) follow the multinomial distribution
with parameters (01, 02, 03).
a. Find a conjugate prior for (01, 02, 03).
b. Define a noninformative prior for (01, 02,
өз).
С. Assume that p(01, 02, Ө3) ос Ө10203. Find
the posterior distribution of (01, 02, 03)
given data y.
Transcribed Image Text:In late October, 1988, a survey was conducted by CBS News of 1500 adults in the United States to find out their preferences in the upcoming presidential election. Out of 1500 persons, y1 = 750 supported George Bush, y2 = 650 supported Michael Dukakis, and y3 = 100 supported other candidates or expressed no opinion. Assume that the data y = (y1,y2,y3) follow the multinomial distribution with parameters (01, 02, 03). a. Find a conjugate prior for (01, 02, 03). b. Define a noninformative prior for (01, 02, өз). С. Assume that p(01, 02, Ө3) ос Ө10203. Find the posterior distribution of (01, 02, 03) given data y.
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